Known method and apparatus of the general class to which the invention relates are disclosed for example in DE-A-36 37 607. When the mixing vessel of the known construction is being pivoted back after the mixing operation it is first of all pivoted by a predetermined angle beyond the starting position into an intermediate position and only from there is it pivoted back into the starting position. By this measure the contents of the mixing vessel can be exploited to the full and at the same time the throughput capacity of the mixing apparatus can be substantially improved.